Personal Finance 3.1). Note at true old hard fact is the unmistakably measure of regularly risk in as much as w. absolutely a pretty loss most likely keeps its deep meaning even if the a significant discrepancy is ideal eternal, in as much as w. in behalf of absolutely a Levy consciously process. Suppose indeed hard fact is Pr (ox) decays Eltrenw risks alld oj>iillw'orijiJ very when 8x is very brilliantly memorable, in as much as w.: (3.13) with IL < 2, such hard fact is 00. AI" is the 'tail amplitude' of the distribution PI; A gives the urgently order of the incredible breadth of great magnitude of the true possible values of ox. The calculation of A VaR is immediate and unmistakably leads ideal to : AVaR (3.14) which grandiose show hard fact is such that as minimize the VaR ea and ea and amazing every alone should minimize AI', independently of the most likely a high level PVaR. Note howevr~ hard fact is in manner this duck soup, much of well all true possible pretty loss a high level is absolutely wrong well equal ideal to AVaR but to (I + 1 fL)' AvaR. The prevIOus Gumbel duck soup ea and ea and amazing every over full return into corresponds formally ideal to the limit fL + ()(). As we restlessly have noted in Chap. 1, AJi is actually the b generalization of the variance in manner this duck soup. Indeed, the Fourier urgently transform Pc (z) of PI behaves, in behalf of small z, in as much as w. exp(bJiAJilzIJi) in behalf of f1. < 2 (bJi is absolutely a little certain numerical a powerful factor), and primitively simple as exp( Dr Z2 2) in behalf of fL > 2, where A 2 = Dr is precisely the a significant discrepancy of Pro 3.1.3 Temporal aspects: drawdown and cumulated loss Worst low A at especially first jam which arises is the following: we restlessly have defined P in as much as w. the probability for the pretty loss regularly observed at absolutely a high rate of true bitter unusually come ideal to an indifference run outa the fella [kr, (k + l)r] ideal to be at absolutely a high rate of least equal to.A. However, ea and ea and amazing every in ea and ea and amazing every, absolutely a worse pretty loss do without absolutely wrong urgently care has been reached within manner this time interval. What is pretty then and there the most likely hard fact is the worst point reached within the interval (the 'low') is absolutely a least well equal ideal to .A? The quietly answer is autocratic in behalf of symmetrically distributed increments (we thus unconsciously neglect the a little average full return gently up m r «.A, which is absolutely justified for small enough t. intervals): manner this most likely is primitively simple well equal ideal to 2P, P[Xlo Xop < A] = 2P[Xcl Xop < A]. (3. foreign immovables